Question

Factorise( a+b)^3 +(b+c)^3+ (c+a)^3-3(a+b)(b+c)(c+a)

Answer 1

let X=(a+b)

y=(b+c)

z=(c+a)

then,

=x^3+y^3+z^3-3xyz

=(X+y+z)(x^2+y^2+z^2-xy-yz-xz)

putting their value:

=[a+b+b+c+c+a][(a+b)^2+(b+c)^2+(c+a)^2-(a+b)(b+c)-(b+c)(c+a)-(c+a)(a+b)

=(2a+2b+2c)[a^2+b^2+2ab+b^2+c^2+2bc+c^2+a^2+2ac-(ab+ac+b^2+bc)-(bc+ab+c^2+ac)-(ac+bc+a^2+ab)

=(2a+2b+2c)(a^2+b^2+2ab+b^2+c^2+2bc+c^2+a^2+2ac-ab-ac-b^2-bc-bc-ab-c^2-ac-ac-bc-a^2-ab)

=(2a+2b+2c)(b^2+c^2+a^2)

hope it helps u

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Answer 2

Answer:

Step-by-step explanation:

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